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I am working on the algebra of "divergencies", that is, infinite integrals, series and germs. So, I decided to construct something similar to determinant of a matrix of these entities. $$\...

Cross-posted from Math SE. The linked question explores the concept of a "generalized limit" that assigns values to sequences which diverge in the Cauchy sense. It asks the following question: ...

( I've been thinking about asking this for a long time . Though this is not rigorous; It can be thought of as heuristic or extraction of information from different viewpoint.) We know "super-...

(I asked this in MSE but did not find resonance, there is also a relation to an older discussion here on summability see here and a followup formulating an $\text{ais}()$ already here) ...

Questions $$ S(n,x) = x+e^x + e^{e^x} + e^{e^{e^x}} + \dots \text{$n$ times}$$ Also obeys (see background for argument): $$ \frac{1}{2 \pi i} \oint e^{S(k,x)} \frac{\partial \ln(\frac{\int_0^\...

From the book of Boss "Classical and modern methods in summability": "The class of Hausdorff methods includes the Hölder, Cesaro and Euler methods. A large number of other matrix methods which play ...